Question 668326
When adding radicals, you must use the same concept as that of adding "like" variables. 


1. add {{{7sqrt(3) + 2sqrt(3)}}}


Since the radicals are the same, simply add the numbers in front of the radicals


{{{7sqrt(3) + 2sqrt(3) =9sqrt(3) }}}


2. add {{{7sqrt(5) + 2sqrt(3)}}}

Since the radicals are not the same, and both are in their simplest form, there is no way to combine these values.  The answer is the same as the problem,

{{{7sqrt(5) + 2sqrt(3)}}} .


But, if the radicals in your problem are different, be sure to check to see if the radicals can be simplified.  Often times, when the radicals are simplified, they become the same radical and can then be added or subtracted.  Always simplify, if possible, before deciding upon your answer.

for example 


3. to add {{{5sqrt(3) + 2sqrt(75)}}} you can simplify {{{sqrt(75)}}} and write it as

{{{sqrt(3*25)=5sqrt(3)}}} 

then you have {{{5sqrt(3) + 2*5sqrt(3)=5sqrt(3) + 10sqrt(3)=15sqrt(3)}}}


4. in this example, each item has the same radicand (6) and the same index (5), so we can collect like terms as follows:

    {{{root(5,6)+4root(5,6)=5root(5,6)}}}

5.This looks ugly, but don't panic.
sometimes you will need to use this rule from before:

    {{{root(m,root(n,a))=root(mn,a)}}}


Now an example:

{{{root(6,root(4,2))+root(12,root(2,2))}}}

{{{root(6*4,2)+root(12*2,2)}}}

{{{root(24,2)+root(24,2)}}}

{{{2root(24,2)}}}
{{{2root(24,2)}}} ≈ {{{2.0586044732869840575647436015478439927405856844283581}}}